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# In mathematics, trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. Trigonometry is also the foundation of surveying.

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##### Boris M.

University of North Carolina at Chapel Hill

##### Shubham P.

University of Washington

##### Martha R.

Michigan State University

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### Video Transcript

draft of a son function. And so we're going to the transformations toe y equals two sun times three omega minus 45 plus one. So let's go ahead and do Our horizontal shift in our horizontal shift is gonna be a 45 degrees and because it's positive we're going to go to the right. So I'm gonna go ahead and I'm gonna do each of these And since my unit's air 45 degrees, we're just gonna move each dot over each point over one unit. So there's my horizontal shift. Now we can do our vertical shift. I'm gonna go ahead and find our midline, which is positive one and our amplitude, which is going to be absolute value of a which is the absolute value of two, which equals two. So we're going to stretch this out So we're gonna come up to blondes from our midline, and we're gonna come down one line, and so we're going to graph this new graph. So if its own zero, it's actually gonna be on the midline, and we're gonna grab this from this purple line so we want to do the purple, do all my points that are on zero first, and then my points that are, um, positive. One will come up here to this positive three. And if their own negative one, they'll actually kind of stay right there. So my graph will look like this. So that is a vertical and horizontal transformation off our function.

Liberty University

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##### Boris M.

University of North Carolina at Chapel Hill

##### Shubham P.

University of Washington

##### Martha R.

Michigan State University